05 MATH40005 REVALIDATED EQUAL DIFFICULTY REPLACEMENT MATRIX
English review edition prepared on 4 October 2026 from a preserved source copy. It is a later presentation, not the historical study interface. Source checks and difficulty judgements describe the original material author's own process; they do not indicate Imperial College London endorsement.
Source SHA-256: 938f4127109c3c38fcf462fafef5464da77a952ce3a9b4a5765084eb8540588bSource date: 2026-08-06
Source page 1
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (8% down the source page)
MATH40005 Equal-difficulty replacement matrix (revalidated version )
English passage 2 (14% down the source page)
This matrix retires the old inference that same topic implies equal difficulty. Each entry states its official-question basis, course method sequence, marks, steps, computation and abstraction / Degree of synthesis and estimated time. Entries without direct official-question references can only be B level methods
method transfer, not labelled as A.
English passage 3 (19% down the source page)
Revised question
marks
Difficulty allocation
Official-question basis
Course method / ability
Number of steps
calculation volume
abstract / integrated
Estimated time
Review conclusion
English passage 4 (21% down the source page)
R1-1(a)
3
A3
2025 Q1(a)(i); 2026 Q1(a)
finite probability-space construction
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 5 (22% down the source page)
3-5 step
low
low / low
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 6 (25% down the source page)
R1-1(b)(ii)
4
B1 C1 D2
2025 Q2(a)(ii)
position-pattern probability
3-5 step
high
Medium / Medium
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 7 (27% down the source page)
R1-1(c)
5
A2 C3
2026 Q1(c); 2020 Q2(c)(i)
support-aware finite/infinite geometric sums
3-5 step
Medium
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 8 (29% down the source page)
R1-1(d)
3
A2 B1
2026 Q2(c)(i)
indicator-to-binomial modelling
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 9 (30% down the source page)
1-3 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 10 (33% down the source page)
R1-2(b)
4
A2 B2
2025 Q2(b)(ii); 2023 Q3(b)(ii)
marginalization on triangular support
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 11 (35% down the source page)
R1-2(c)
3
A1 B2
2025 Q2(b)(iii); 2022 Q3(c)(iii)
conditional-density ratio and support
1-3 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 12 (37% down the source page)
R1-2(d)
2
A2
2025 Q2(b)(iv); 2023 Q3(b)(iii)
support/factorization test for independence
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 13 (38% down the source page)
R1-2(e)
5
B1 C1 D3
2024 Q2(b)(vi); 2022 Q2(b)
joint LOTUS moments and covariance
3-5 step
high
high / high
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 14 (40% down the source page)
R1-2(f)
3
D3
2021 Q3(c)(iii); 2023 Q3(b)(iv)
CDF method for a ratio on triangular support
1-3 step
high
high / high
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 15 (42% down the source page)
R1-3(a)
3
A3
2024 Q4(a); 2026 Q3(a)
mean/median loss minimizers
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 16 (44% down the source page)
R1-3(b)
3
A2 B1
2023 Q4(a); 2026 Q3(b)
bias-variance identity
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 17 (45% down the source page)
R1-3(c)
4
A2 B2
2020 Q6(a)(ii); 2024 Q4(c)(i)
unknown-variance t confidence interval
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 18 (47% down the source page)
R1-3(d)
5
A2 B1 C2
2021 Q5(b)(i)-(iii); 2026 Q3(d)(ii)
one-sample t test and p-value
3-5 step
Medium
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 19 (49% down the source page)
3-5 step
Medium
Medium / Medium
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 20 (52% down the source page)
R1-4(a)
4
A2 B2
2023 Q5(c); 2026 Q4(a)
covariance algebra for linear combinations
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 21 (53% down the source page)
3-5 step
high
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 22 (56% down the source page)
R1-4(c)
4
A1 C1 D2
2021 Q6(c); 2025 Q4(d); 2026 Q4(b)
residual diagnosis and transformation
3-5 step
high
Medium / Medium
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 23 (58% down the source page)
R1-4(d)
5
C1 D4
2026 Q4(f)
support-dependent non-unique MLE
3-5 step
high
high / high
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 24 (60% down the source page)
bootstrap sample definition
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 25 (62% down the source page)
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 26 (65% down the source page)
R2-1(b)
3
A2 B1
2025 Q1(b)(ii)
Bayes reversal after total probability
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 27 (67% down the source page)
R2-1(c)
4
B1 C1 D2
2025 Q1(b)(iii)
Bayes under a changed mechanism
3-5 step
high
Medium / Medium
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 28 (69% down the source page)
R2-1(d)
5
A2 B2 C1
2025 Q2(a)(i)
multitype password count
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 29 (70% down the source page)
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 30 (73% down the source page)
R2-2(a)
4
A3 B1
2025 Q3(a)(i)
inverse-transform/CDF method
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 31 (75% down the source page)
R2-2(b)
4
A3 B1
2025 Q3(a)(ii)
order-statistic CDF
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 32 (77% down the source page)
R2-2(c)
4
A1 B1 C1 D1
2025 Q3(b)(i)
MGF derivation by completing the square
3-5 step
Medium
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 33 (78% down the source page)
R2-2(d)
4
A1 B1 C1 D1
2025 Q3(b)(ii)
MGF product and distribution identification
3-5 step
Medium
Medium / Medium
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 34 (80% down the source page)
R2-2(e)
4
B1 C1 D2
2025 Q3(c)(i)
moment determinacy via MGF existence
3-5 step
high
Medium / Medium
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 35 (82% down the source page)
R2-3(a)
2
A2
2025 Q4(a)(i)
variance of an independent sample mean
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 36 (83% down the source page)
R2-3(b)
6
A1 B2 C1 D2
2025 Q4(a)(ii)
expectation of sample variance under unequal means 5-8 step
high
Medium / Medium
9 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 37 (85% down the source page)
R2-3(c)
4
A3 B1
2025 Q4(b)(i)
Student-t confidence interval
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 38 (87% down the source page)
R2-3(d)
4
A2 B1 C1
2025 Q4(b)(ii)
chi-square variance interval
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 39 (89% down the source page)
R2-3(e)
4
A1 C1 D2
2025 Q4(d); 2023 Q6(d)(ii)
Q-Q diagnostic
3-5 step
high
Medium / Medium
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 40 (90% down the source page)
R2-4(a)
5
A1 B1 C1 D2
2025 Q6(a)
two-boundary support-dependent MLE
3-5 step
high
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
Source page 2
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (8% down the source page)
Revised question
marks
Difficulty allocation
Official-question basis
Course method / ability
Number of steps
calculation volume
abstract / integrated
Estimated time
Review conclusion
English passage 2 (10% down the source page)
R2-4(b)
4
A1 B1 C1 D1
2025 Q6(b)(i)-(iii)
regression-estimator covariance
3-5 step
Medium
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 3 (12% down the source page)
R2-4(c)
4
A1 B2 C1
2025 Q6(c)
percentile bootstrap interval
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 4 (13% down the source page)
R2-4(d)
7
A2 B1 C1 D3
2025 Q5(b)
known-variance two-sample z test with p-value
5-8 step
high
high / high
10 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 5 (15% down the source page)
R3-1(a)
5
A3 B2
2023 Q1(a)
birthday collision complement
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 6 (17% down the source page)
R3-1(b)
5
A1 B1 C1 D2
2023 Q1(b)
exact single-collision count
3-5 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 7 (18% down the source page)
R3-1(c)
5
A3 B2
2023 Q1(c)
diagnostic Bayes calculation
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 8 (20% down the source page)
R3-1(d)
5
A1 B1 C1 D2
2023 Q1(d)
measurability of a piecewise discrete variable
3-5 step
high
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 9 (22% down the source page)
R3-2(a)
4
A2 C1 D1
2023 Q3(a)
dependence counterexample for Poisson sums
3-5 step
Medium
Medium / Medium
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 10 (24% down the source page)
5-8 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 11 (26% down the source page)
3-5 step
Medium
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 12 (29% down the source page)
Poisson splitting via joint pmf
3-5 step
low
low / low
8 minutes
Retain as B level transfer: methods relate to official questions, without directly copying the question type
English passage 13 (32% down the source page)
R3-3(a)
8
A5 B2 D1
2023 Q3(b)(i)-(iii)
curved-support normalization and marginalization
5-8 step
low
low / low
11 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 14 (34% down the source page)
R3-3(b)
5
A1 B1 C1 D2
2023 Q3(b)(iv)
conditional CDF on curved support
3-5 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 15 (36% down the source page)
R3-3(c)
7
A3 B2 C1 D1
2023 Q3(c)
monotone CDF transform plus LOTUS
5-8 step
Medium
Medium / Medium
9 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 16 (37% down the source page)
5-8 step
high
Medium / Medium
10 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 17 (40% down the source page)
R3-4(b)
5
A2 B1 C1 D1
2024 Q5(b)
exact hypergeometric tail test
3-5 step
Medium
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 18 (42% down the source page)
R3-4(c)
4
A1 B1 C2
2020 Q6(a)(i); 2023 Q4(c)(i)
known-variance z confidence interval
3-5 step
Medium
Medium / Medium
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 19 (43% down the source page)
R3-4(d)
3
A1 B1 C1
2023 Q4(c)(ii); 2024 Q6(a)
frequentist confidence interpretation
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 20 (45% down the source page)
R4-1(a)
3
A3
2020 Q1(a)
sigma-algebra definition
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 21 (47% down the source page)
R4-1(b)
3
A3
2020 Q1(b)
probability-measure definition
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 22 (49% down the source page)
R4-1(c)
4
A2 B1 D1
2020 Q1(e)
positive stars and bars
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 23 (50% down the source page)
R4-1(d)
4
A1 B2 C1
2022 Q1(b)(i)
binomial identity proof
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 24 (52% down the source page)
R4-1(e)
6
B2 C1 D3
2022 Q1(b)(ii)
double counting/story proof
5-8 step
high
high / high
9 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 25 (54% down the source page)
R4-2(a)
4
A4
2020 Q2(b)
piecewise discrete CDF
3-5 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 26 (56% down the source page)
R4-2(b)
6
A2 B2 C1 D1
2020 Q2(c)(ii)
minimum of independent geometric waits
5-8 step
Medium
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 27 (57% down the source page)
R4-2(c)
6
A1 B1 C1 D3
2020 Q2(d)
pattern waiting by states/geometric stages
5-8 step
high
high / high
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 28 (59% down the source page)
R4-2(d)
4
A1 B2 C1
2020 Q3(d)(ii)
proof of total expectation
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 29 (61% down the source page)
R4-3(a)
6
A3 B2 C1
2022 Q4(a)(i)-(ii); 2020 Q4(a)(iv)-(v)
bias/variance/MSE of an estimator
5-8 step
low
low / low
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 30 (63% down the source page)
R4-3(b)
4
A2 B2
2020 Q4(b)
indicator proof of Markov inequality
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 31 (64% down the source page)
R4-3(c)
5
A1 B1 C1 D2
2022 Q4(b); 2023 Q4(b)
distribution-free sample-size guarantee
3-5 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 32 (66% down the source page)
R4-3(d)
5
A2 B1 C1 D1
2020 Q4(c); 2022 Q5(c)
Bonferroni correction
3-5 step
Medium
Medium / Medium
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 33 (68% down the source page)
R4-4(a)
6
A3 B2 C1
2020 Q5(b); 2023 Q6(b)
OLS derivation
5-8 step
low
low / low
9 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 34 (69% down the source page)
R4-4(b)
5
A1 B1 C1 D2
2020 Q5(d)
boundary MLE
3-5 step
high
Medium / Medium
7 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 35 (71% down the source page)
Gamma conjugate update
3-5 step
Medium
Medium / Medium
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 36 (74% down the source page)
R4-4(d)
5
A2 C1 D2
2020 Q6(d)
non-trivial variance lower bound
3-5 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 37 (76% down the source page)
R5-1(a)
2
A2
2023 Q2(a)(i)
indicator/preimage identity
1-3 step
low
low / low
3 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 38 (77% down the source page)
R5-1(b)
6
A2 B2 D2
2023 Q2(a)(ii)
preimage sigma-algebra proof
5-8 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 39 (79% down the source page)
R5-1(c)
4
A2 B1 C1
2026 Q2(a)
pairwise-versus-mutual independence construction
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 40 (81% down the source page)
R5-1(d)
4
A2 B1 C1
2020 Q2(a); 2022 Q1(a)(ii)
finite-space measurability check
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 41 (83% down the source page)
R5-1(e)
4
A2 B2
2021 Q1(b)(i)-(iii)
product probability space and power set
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 42 (84% down the source page)
R5-2(a)
7
A1 B1 C2 D3
2021 Q2(d)
MGF of a scale mixture
5-8 step
high
high / high
10 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 43 (86% down the source page)
R5-2(b)
6
A2 B2 D2
2022 Q2(c)(i)
continuous-discrete mixture transform
5-8 step
high
Medium / Medium
9 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 44 (88% down the source page)
R5-2(c)
7
A2 B1 C1 D3
2020 Q3(c)
three-dimensional normalization and LOTUS
5-8 step
high
high / high
10 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 45 (90% down the source page)
R5-3(a)
5
A2 B1 C1 D1
2024 Q5(b) variant
exact hypergeometric test
3-5 step
Medium
Medium / Medium
7 minutes
Retain as B level transfer: methods relate to official questions, without directly copying the question type
Source page 3
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (8% down the source page)
Revised question
marks
Difficulty allocation
Official-question basis
Course method / ability
Number of steps
calculation volume
abstract / integrated
Estimated time
Review conclusion
English passage 2 (10% down the source page)
R5-3(b)
4
A2 B1 C1
2023 Q4(d)
quartiles and Tukey outliers
3-5 step
low
low / low
6 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 3 (12% down the source page)
R5-3(c)
3
A1 B1 C1
2021 Q6(d); 2023 Q5(d)
Simpson reversal/confounding
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 4 (13% down the source page)
R5-3(d)
5
A1 B1 C1 D2
2021 Q4(b)
Chebyshev sample-size design
3-5 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 5 (15% down the source page)
R5-3(e)
3
A1 B1 C1
2022 Q5(a); 2025 Q5(c)
testing error trade-off
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 6 (17% down the source page)
R5-4(a)
6
A2 B1 C1 D2
2022 Q6(a)
regular log-likelihood MLE
5-8 step
high
Medium / Medium
8 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 7 (18% down the source page)
R5-4(b)
4
A3 B1
2022 Q6(d)
OLS mean-point property
3-5 step
low
low / low
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 8 (20% down the source page)
R5-4(c)
4
A1 B1 C1 D1
2025 Q3(c)(i)
moment determinacy
3-5 step
Medium
Medium / Medium
5 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 9 (22% down the source page)
R5-4(d)
3
A2 B1
2025 Q6(c)
bootstrap percentile interval
1-3 step
low
low / low
4 minutes
Retain: supported by official solution methods and marks / Steps / Reconciled time budget
English passage 10 (24% down the source page)
R5-4(e)
3
A2 B1
2021 Q4(a)(iii)
constructing an unbiased estimator
1-3 step
low
low / low
5 minutes
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English passage 11 (25% down the source page)
R6-1(a)
6
A2 B2 C1 D1
2022 Q1(b) method, altered parameter
algebraic and narrative double counting
5-8 step
Medium
Medium / Medium
9 minutes
Retain as B level transfer: methods relate to official questions, without directly copying the question type
English passage 12 (27% down the source page)
R6-1(b)
6
A2 B2 C1 D1
2022 Q3(a); 2024 Q1(c)
Bayes/base-rate transfer
5-8 step
Medium
Medium / Medium
8 minutes
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English passage 13 (29% down the source page)
R6-1(c)
5
A1 B1 C1 D2
2023 Q1(b)
exact birthday collision
3-5 step
high
Medium / Medium
7 minutes
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English passage 14 (31% down the source page)
R6-1(d)
3
A3
2025 Q1(a)(i); 2021 Q1(b)
finite product probability space
1-3 step
low
low / low
3 minutes
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English passage 15 (32% down the source page)
R6-2(a)
8
A4 B2 C1 D1
2022 Q3(c)(i)-(iii)
conditional expectation on triangular support
5-8 step
Medium
Medium / Medium
11 minutes
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English passage 16 (34% down the source page)
R6-2(b)
7
A2 B2 C1 D2
2024 Q3(b)(ii)-(iii)
compound-Poisson moments
5-8 step
high
Medium / Medium
9 minutes
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English passage 17 (36% down the source page)
R6-2(c)
5
A2 B1 C1 D1
2025 Q3(a); historical transformation chain
order statistic followed by monotone transform
3-5 step
Medium
Medium / Medium
7 minutes
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English passage 18 (38% down the source page)
R6-3(a)
6
A1 B2 C1 D2
2025 Q4(a)(i)-(ii)
non-identical-normal sample variance expectation
5-8 step
high
Medium / Medium
8 minutes
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English passage 19 (39% down the source page)
R6-3(b)
7
A2 B2 C1 D2
2023 Q5(b)
pooled two-sample t test for a linear combination
5-8 step
high
Medium / Medium
10 minutes
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English passage 20 (41% down the source page)
R6-3(c)
4
A2 B1 C1
2026 Q3(d)(i)
chi-square variance interval
3-5 step
low
low / low
5 minutes
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English passage 21 (43% down the source page)
1-3 step
low
low / low
5 minutes
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English passage 22 (46% down the source page)
R6-4(a)
5
A2 B1 C1 D1
2024 Q6(c)
least squares for a transformed predictor
3-5 step
Medium
Medium / Medium
7 minutes
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English passage 23 (47% down the source page)
1-3 step
low
low / low
4 minutes
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English passage 24 (50% down the source page)
R6-4(c)
5
A2 B1 C1 D1
2026 Q4(f)
non-unique support MLE
3-5 step
Medium
Medium / Medium
7 minutes
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English passage 25 (52% down the source page)
R6-4(d)
4
A1 B1 C1 D1
2021 Q6(b)
Beta-geometric conjugacy
3-5 step
Medium
Medium / Medium
6 minutes
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English passage 26 (53% down the source page)
R6-4(e)
3
A2 B1
2024 Q5(d); 2026 Q4(d)
spurious correlation interpretation
1-3 step
low
low / low
4 minutes
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Source page 4
